Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number...
13 KB (1,370 words) - 18:05, 24 January 2025
mathematics, nonstandard calculus is the modern application of infinitesimals, in the sense of nonstandard analysis, to infinitesimal calculus. It provides a rigorous...
25 KB (3,981 words) - 00:52, 10 February 2025
Robinson's infinitesimals include texts by Stroyan (dating from 1972) and Howard Jerome Keisler (Elementary Calculus: An Infinitesimal Approach). Students...
37 KB (5,092 words) - 16:24, 23 May 2025
Nonstandard analysis (section Applications to calculus)
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard...
31 KB (3,978 words) - 00:54, 22 April 2025
Differential (mathematics) (redirect from Differential (infinitesimal))
related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions....
27 KB (3,994 words) - 18:39, 27 May 2025
of calculus Generality of algebra Elementary Calculus: An Infinitesimal Approach Nonstandard calculus Infinitesimal Archimedes' use of infinitesimals For...
4 KB (389 words) - 12:14, 10 February 2024
Elementary calculus may refer to: The elementary aspects of differential and integral calculus; Elementary Calculus: An Infinitesimal Approach, a textbook...
214 bytes (55 words) - 10:03, 28 December 2019
Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series...
55 KB (6,777 words) - 16:36, 30 May 2025
formulation of the transfer principle is Keisler's book Elementary Calculus: An Infinitesimal Approach. Every real x {\displaystyle x} satisfies the inequality...
18 KB (2,686 words) - 16:19, 23 May 2025
arithmetic in the sense of Skolem. Howard Jerome Keisler: Elementary Calculus: An Infinitesimal Approach. First edition 1976; 2nd edition 1986. This book is...
2 KB (294 words) - 10:37, 22 November 2024
Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former...
76 KB (8,805 words) - 06:25, 7 June 2025
Division by zero (section Calculus)
al. 2012, p. 292 Keisler, H. Jerome (2023) [1986], Elementary Calculus: An Infinitesimal Approach, Prindle, Weber & Schmidt, pp. 29–30 Conway, John H...
42 KB (5,688 words) - 19:44, 7 June 2025
Leibniz's notation (category Mathematics of infinitesimals)
first-year calculus textbook, Elementary calculus: an infinitesimal approach, based on Robinson's approach. From the point of view of modern infinitesimal theory...
24 KB (3,099 words) - 02:27, 2 May 2025
representing an infinitesimally small quantity, Keisler published Elementary Calculus: An Infinitesimal Approach, a first-year calculus textbook conceptually...
5 KB (513 words) - 12:28, 20 January 2025
Isaac Newton (category History of calculus)
Hall 1980, pp. 1, 15, 21. H. Jerome Keisler (2013). Elementary Calculus: An Infinitesimal Approach (3rd ed.). Dover Publications. p. 903. ISBN 978-0-486-31046-6...
171 KB (18,277 words) - 15:25, 6 June 2025
Hyperreal number (category Mathematics of infinitesimals)
Hyperreals. A gentle introduction. Keisler, Elementary Calculus: An Approach Using Infinitesimals. Includes an axiomatic treatment of the hyperreals, and...
33 KB (4,924 words) - 01:41, 9 June 2025
Differential of a function (category Differential calculus)
ISBN 978-0-19-506136-9 Keisler, H. Jerome (1986), Elementary Calculus: An Infinitesimal Approach (2nd ed.). Kock, Anders (2006), Synthetic Differential...
32 KB (4,766 words) - 00:09, 31 May 2025
Derivative (redirect from Derivative (calculus))
version here. Keisler, H. Jerome (2012) [1986], Elementary Calculus: An Approach Using Infinitesimals (2nd ed.), Prindle, Weber & Schmidt, ISBN 978-0-871-50911-6...
57 KB (7,280 words) - 04:41, 1 June 2025
analysis Non-standard calculus Hyperinteger Hyperreal number Transfer principle Overspill Elementary Calculus: An Infinitesimal Approach Criticism of non-standard...
14 KB (1,012 words) - 00:08, 16 November 2024
one. Multivariable calculus may be thought of as an elementary part of calculus on Euclidean space. The special case of calculus in three dimensional...
19 KB (2,369 words) - 14:23, 7 June 2025
infinitesimals, an operation that we would now call integration. The origins of differentiation likewise predate the fundamental theorem of calculus by...
31 KB (4,883 words) - 12:15, 2 May 2025
Integral (redirect from Integral calculus)
Elementary Calculus: An Approach Using Infinitesimals, University of Wisconsin Stroyan, K. D., A Brief Introduction to Infinitesimal Calculus, University...
69 KB (9,288 words) - 18:38, 23 May 2025
bends, or cusps. differential (infinitesimal) The term differential is used in calculus to refer to an infinitesimal (infinitely small) change in some...
88 KB (10,926 words) - 07:11, 7 March 2025
Standard part function (category Calculus)
1007/978-1-4612-0615-6. ISBN 978-0-387-98464-3. H. Jerome Keisler. Elementary Calculus: An Infinitesimal Approach. First edition 1976; 2nd edition 1986. (This book is...
7 KB (1,079 words) - 03:30, 3 December 2024
Bishop reviewed the book Elementary Calculus: An Infinitesimal Approach by Howard Jerome Keisler, which presented elementary calculus using the methods of...
28 KB (3,520 words) - 13:42, 3 July 2024
Increment theorem (category Theorems in calculus)
Nonstandard calculus Elementary Calculus: An Infinitesimal Approach Abraham Robinson Taylor's theorem Howard Jerome Keisler: Elementary Calculus: An Infinitesimal...
2 KB (333 words) - 23:57, 8 July 2023
Extreme value theorem (category Theorems in calculus)
89–90. ISBN 0-07-054235-X. Keisler, H. Jerome (1986). Elementary Calculus : An Infinitesimal Approach (PDF). Boston: Prindle, Weber & Schmidt. p. 164. ISBN 0-87150-911-3...
22 KB (3,926 words) - 10:22, 17 May 2025
Meanwhile, calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the study of continuous change. Discrete calculus has two...
39 KB (6,577 words) - 14:32, 2 June 2025
Cavalieri's principle (category History of calculus)
Evangelista Torricelli's and John Wallis's infinitesimals was a major advance in the history of calculus. The indivisibles were entities of codimension...
15 KB (1,966 words) - 13:34, 1 May 2025
Whereas elementary calculus is about infinitesimally small changes in the values of functions without changes in the function itself, calculus of variations...
58 KB (9,530 words) - 08:36, 5 June 2025